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Adaptive Filtering Using Channel Representations

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Mathematical Methods for Signal and Image Analysis and Representation

Part of the book series: Computational Imaging and Vision ((CIVI,volume 41))

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Abstract

This review article gives an overview on adaptive filtering methods based on channel representations. The framework of channel representations and its relation to density estimation is introduced. The fast and accurate scheme of virtual shift decoding is introduced and applied in several variants of channel smoothing:

  • channel smoothing with alpha-synthesis for improving stability of edge-enhancing filtering

  • orientation adaptive channel smoothing with applications to coherence-enhancing filtering

  • channel smoothing using graph-cuts for improving filtering results at corners

  • channel-coded feature maps (CCFMs) which lead to a significant speed-up of channel averaging

  • CCFM-based smoothing based on optimal parameters derived from a novel uncertainty relation

For each method, an algorithmic description and some examples of results are provided, together with discussions and references of the original papers. Cross connections to other articles in this volume are given where appropriate.

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Acknowledgements

The author would like to thank P.-E. Forssén for various discussions about the paper, in particular on alpha-synthesis. The research leading to these results has received funding from the European Community’s Seventh Framework Programme (FP7/2007-2013) under grant agreements no 215078 (DIPLECS) and 247947 (GARNICS) as well as the VR project 2009-4282.

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Authors and Affiliations

  1. Computer Vision Laboratory, Department of Electrical Engineering, Linköping University, 58183, Linköping, Sweden

    Michael Felsberg

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  1. Michael Felsberg
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Correspondence to Michael Felsberg .

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Editors and Affiliations

  1. Dept. Mathematics & Computer Science, Eindhoven University of Technology, Eindhoven, 5600 MB, The Netherlands

    Luc Florack

  2. Dept. Mathematics & Computer Science, Eindhoven University of Technology, P.O. Box 513, Eindhoven, 5600 MB, The Netherlands

    Remco Duits

  3. Dept. Applied Mathematics, Delft University of Technology, Delft, 2628 CD, The Netherlands

    Geurt Jongbloed

  4. Probability & Stochastic Networks (PNA), Centrum Wiskunde & Informatica, Amsterdam, 1098 XG, The Netherlands

    Marie-Colette van Lieshout

  5. Fakultät für Mathematik, Universität Duisburg-Essen, Essen, 45141, Germany

    Laurie Davies

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Felsberg, M. (2012). Adaptive Filtering Using Channel Representations. In: Florack, L., Duits, R., Jongbloed, G., van Lieshout, MC., Davies, L. (eds) Mathematical Methods for Signal and Image Analysis and Representation. Computational Imaging and Vision, vol 41. Springer, London. https://doi.org/10.1007/978-1-4471-2353-8_2

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